It can be deep, complex, simple, fun, easy to play hard to master, whichever kind of cooperation -> leading to more synergy, dare I say symbiosis between the players!
Ok, random idea that just popped in my brain: You could have a cooperative game where the goal is to handle nutrients, etc. in order to cooperatively build a baby inside's a female womb. Basically, it would be about achieving "life" by cooperating: repelling microbes, driving whatever fluids/vitamins/hormones are needed to the right places, etc. etc.